Question

What is the frequency of the fundamental mode of vibration of a steel piano wire stretched to a tension of 440 N? The wire is 0.630 m long and has a mass of 5.69 g.

Answer 1

220.698Hz

Step-by-step explanation:

The fundamental frequency f₀ is expressed as f₀ =V/2L where;

V is the speed of the string =
`\sqrt{(T)/(M) }`

m is the mass of the string

L is the length of the string

T is the tension in the string

f₀ =
`(1)/(2L) \sqrt{(T)/(m) }`

Given datas

m = 5.69g = 0.00569 kg

T = 440N

L = 0.630 m

Required

Fundamental frequency of the steel piano wire f₀

`f_0 = (1)/(2(0.630))\sqrt{(440)/(0.00569) } \\ \\f_0 = (1)/(1.26)√(77,328.65 ) \\\\f_0 = (1)/(1.26) * 278.08\\\\f_0 = 220.698Hz`

Hence the frequency of the fundamental mode of vibration of the steel piano wire stretched to a tension of 440N is 220.698Hz